I have used 2 different models of brother laser printers with Arch, both running impeccably.
It seems to me you went the convoluted way about it. Aur packs specific drivers for brother printers, no need to fuss around with .deb packages.
Check the Arch wiki to identify the driver you need.
https://wiki.archlinux.org/index.php/CUPS/Printer-specific_problems#Brother
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